Conversion Factors for the Cumulative Average Number of Direct Labor Hours per Unit
\(\begin{array}{c}
\begin{array}{c}
80 \% \text { Learning Rate }\
\text { ( } n=\text { cumulative production) }\
\begin{array}{rrrrrr}
\hline n & & n & & {n} & \
\hline 1 & 1.00000 & 19 & 0.53718 & 37 & 0.43976 \
2 & 0.90000 & 20 & 0.52425 & 38 & 0.43634 \
3 & 0.83403 & 21 & 0.51715 & 39 & 0.43304 \
4 & 0.78553 & 22 & 0.51045 & 40 & 0.42984 \
5 & 0.74755 & 23 & 0.50410 & 64 & 0.37382 \
6 & 0.71657 & 24 & 0.49808 & 128 & 0.30269 \
7 & 0.69056 & 25 & 0.49234 & 256 & 0.24405 \
8 & 0.66824 & 26 & 0.48688 & 512 & 0.19622 \
9 & 0.64876 & 27 & 0.48167 & 600 & 0.18661 \
10 & 0.63154 & 28 & 0.47668 & 700 & 0.17771 \
11 & 0.61613 & 29 & 0.47191 & 800 & 0.17034 \
12 & 0.60224 & 30 & 0.46733 & 900 & 0.16408 \
13 & 0.58960 & 31 & 0.46293 & 1,000 & 0.15867 \
14 & 0.57802 & 32 & 0.45871 & 1,200 & 0.14972 \
15 & 0.56737 & 33 & 0.46464 & 1,400 & 0.14254 \
16 & 0.55751 & 34 & 0.45072 & 1,600 & 0.13660 \
17 & 0.54834 & 35 & 0.44694 & 1,800 & 0.13155\
18& 0.53979 & 36 & 0.44329 & 2,000 & 0.12720
\end{array}
\end{array}
\begin{array}{cl}
90 \% \text { Learning Rate }\
\text { ( } n=\text { cumulative production) }\
\begin{array}{rrrrrr}
\hline n &&{n} & &n & \
\hline 1 & 1.00000 & 19 & 0.73545 & 37 & 0.67091 \
2 & 0.95000 & 20 & 0.73039 & 38 & 0.66839 \
3 & 0.91540 & 21 & 0.72559 & 39 & 0.66595 \
4 & 0.88905 & 22 & 0.72102 & 40 & 0.66357 \
5 & 0.86784 & 23 & 0.71666 & 64 & 0.62043 \
6 & 0.85013 & 24 & 0.71251 & 128 & 0.56069 \
7 & 0.83496 & 25 & 0.70853 & 256 & 0.50586 \
8 & 0.82172 & 26 & 0.70472 & 512 & 0.45594 \
9 & 0.80998 & 27 & 0.70106 & 600 & 0.44519 \
10 & 0.79945 & 28 & 0.69754 & 700 & 0.43496 \
11 & 0.78991 & 29 & 0.69416 & 800 & 0.42629 \
12 & 0.78120 & 30 & 0.69090 & 900 & 0.41878 \
13 & 0.77320 & 31 & 0.68775 & 1,000 & 0.41217 \
14 & 0.76580 & 32 & 0.67471 & 1,200 & 0.40097 \
15 & 0.75891 & 33 & 0.68177 & 1,400 & 0.39173 \
16 & 0.75249 & 34 & 0.67893 & 1,600 & 0.38390 \
17 & 0.74646 & 35 & 0.67617 & 1,800 & 0.37711 \
18 & 0.74080 & 36 & 0.67350 & 2,000 & 0.37114
\end{array}
\end{array}
\end{array}\)

-How long will it take to make units 11 through 20 if the first one took 8 hours and there is a 90 percent learning rate? Refer to the copy of Table G.1 above.
A) Fewer than or equal to 50 hours
B) Greater than 50 hours but fewer than or equal to 55 hours
C) Greater than 55 hours but fewer than or equal to 60 hours
D) Greater than 60 hours

Question

Conversion Factors for the Cumulative Average Number of Direct Labor Hours per Unit
\(\begin{array}{c}
\begin{array}{c}
80 \% \text { Learning Rate }\
\text { ( } n=\text { cumulative production) }\
\begin{array}{rrrrrr}
\hline n & & n & & {n} & \
\hline 1 & 1.00000 & 19 & 0.53718 & 37 & 0.43976 \
2 & 0.90000 & 20 & 0.52425 & 38 & 0.43634 \
3 & 0.83403 & 21 & 0.51715 & 39 & 0.43304 \
4 & 0.78553 & 22 & 0.51045 & 40 & 0.42984 \
5 & 0.74755 & 23 & 0.50410 & 64 & 0.37382 \
6 & 0.71657 & 24 & 0.49808 & 128 & 0.30269 \
7 & 0.69056 & 25 & 0.49234 & 256 & 0.24405 \
8 & 0.66824 & 26 & 0.48688 & 512 & 0.19622 \
9 & 0.64876 & 27 & 0.48167 & 600 & 0.18661 \
10 & 0.63154 & 28 & 0.47668 & 700 & 0.17771 \
11 & 0.61613 & 29 & 0.47191 & 800 & 0.17034 \
12 & 0.60224 & 30 & 0.46733 & 900 & 0.16408 \
13 & 0.58960 & 31 & 0.46293 & 1,000 & 0.15867 \
14 & 0.57802 & 32 & 0.45871 & 1,200 & 0.14972 \
15 & 0.56737 & 33 & 0.46464 & 1,400 & 0.14254 \
16 & 0.55751 & 34 & 0.45072 & 1,600 & 0.13660 \
17 & 0.54834 & 35 & 0.44694 & 1,800 & 0.13155\
18& 0.53979 & 36 & 0.44329 & 2,000 & 0.12720
\end{array}
\end{array}
\begin{array}{cl}
90 \% \text { Learning Rate }\
\text { ( } n=\text { cumulative production) }\
\begin{array}{rrrrrr}
\hline n &&{n} & &n & \
\hline 1 & 1.00000 & 19 & 0.73545 & 37 & 0.67091 \
2 & 0.95000 & 20 & 0.73039 & 38 & 0.66839 \
3 & 0.91540 & 21 & 0.72559 & 39 & 0.66595 \
4 & 0.88905 & 22 & 0.72102 & 40 & 0.66357 \
5 & 0.86784 & 23 & 0.71666 & 64 & 0.62043 \
6 & 0.85013 & 24 & 0.71251 & 128 & 0.56069 \
7 & 0.83496 & 25 & 0.70853 & 256 & 0.50586 \
8 & 0.82172 & 26 & 0.70472 & 512 & 0.45594 \
9 & 0.80998 & 27 & 0.70106 & 600 & 0.44519 \
10 & 0.79945 & 28 & 0.69754 & 700 & 0.43496 \
11 & 0.78991 & 29 & 0.69416 & 800 & 0.42629 \
12 & 0.78120 & 30 & 0.69090 & 900 & 0.41878 \
13 & 0.77320 & 31 & 0.68775 & 1,000 & 0.41217 \
14 & 0.76580 & 32 & 0.67471 & 1,200 & 0.40097 \
15 & 0.75891 & 33 & 0.68177 & 1,400 & 0.39173 \
16 & 0.75249 & 34 & 0.67893 & 1,600 & 0.38390 \
17 & 0.74646 & 35 & 0.67617 & 1,800 & 0.37711 \
18 & 0.74080 & 36 & 0.67350 & 2,000 & 0.37114
\end{array}
\end{array}
\end{array}\)

-How long will it take to make units 11 through 20 if the first one took 8 hours and there is a 90 percent learning rate? Refer to the copy of Table G.1 above.
A) Fewer than or equal to 50 hours
B) Greater than 50 hours but fewer than or equal to 55 hours
C) Greater than 55 hours but fewer than or equal to 60 hours
D) Greater than 60 hours

Quizplus · Accepted Answer

From the table, we can find the conversion factor for the 1st unit being 1.0. For the 11th unit, with a 90% learning rate, the cumulative production would be 0.61613, and the corresponding conversion factor would be 0.47191.
The cumulative production for the 20th unit would be 0.73039, and the corresponding conversion factor would be 0.69754. 
Using the cumulative average number of direct labor hours per unit formula:

Cumulative average number of direct labor hours per unit = (First unit labor hours) x (Cumulative factor for n-1th unit) / (Cumulative factor for nth unit)

For the 11th unit: 
Cumulative average number of direct labor hours per unit = (8) x (1) / (0.47191) = 16.95

For the 20th unit: 
Cumulative average number of direct labor hours per unit = (8) x (0.73039) / (0.69754) = 8.42

Therefore, the total time to make the 11th to 20th unit would be: 
Total time = (number of units) x (average labor hours per unit) 
Total time = 10 x (16.95 + 8.42) = 253.7 hours, which is greater than 50 hours but fewer than or equal to 55 hours. Thus, the answer is B.